Energetic events at the Large Hadron Collider (LHC) consist of hundreds of particles each described by four momentum components, leading to embedding spaces with dimensionality \(\mathcal {O}(1000)\) . Dimensionality reduction is therefore critically important for understanding this data. Distance measures between events based on optimal transport, most notably Earth Movers Distance (EMD), have been introduced for usage on particle physics datasets in recent years [1]}, [2]}, [3]}, [4]}, [5]}, leading to geometric interpretations of the data manifold. Different generative processes involved in creating events are associated with hierarchically distinct EMD scales.
